A note on the Catalan-Dickson conjecture

Author:
H. J. J. te Riele

Journal:
Math. Comp. **27** (1973), 189-192

MSC:
Primary 10A40

DOI:
https://doi.org/10.1090/S0025-5718-1973-0325522-5

Corrigendum:
Math. Comp. **27** (1973), 1011-1012.

MathSciNet review:
0325522

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, the existence of an aliquot sequence with more than 5092 monotonically increasing even terms is proved; the first 125 terms are listed.

**[1]**J. D. Alanen,*Empirical Study of Aliquot Series*, Ph.D. Thesis, Yale University, New Haven, Conn., 1972.**[2]**E. Catalan, "Propositions et questions diverses,"*Bull. Soc. Math. France*, v. 16, 1887/88, pp. 128-129. MR**1504036****[3]**H. Cohen, "On amicable and sociable numbers,"*Math. Comp.*, v. 24, 1970. pp. 423-429. MR**42**#5887. MR**0271004 (42:5887)****[4]**L. E. Dickson, "Theorems and tables on the sum of the divisors of a number,"*Quart. J. Pure Appl. Math.*, v. 44, 1913, pp. 264-296.**[5]**R. K. Guy & J. L. Selfridge, "Interim report on aliquot series,"*Proc. Winnipeg Conf. on Numerical Math.*, Oct. 1971. MR**0335412 (49:194)****[6]**D. H. Lehmer, private communication.**[7]**G. A. Paxson,*Annapolis meeting of the Math. Assoc. of America*, May 5th, 1956.**[8]**B. Tuckerman, "The 24th Mersenne prime,"*Notices Amer. Math. Soc.*, v. 18, 1971, p. 608. Abstract #684-A15. MR**0291072 (45:166)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0325522-5

Keywords:
Aliquot sequence,
Catalan-Dickson conjecture

Article copyright:
© Copyright 1973
American Mathematical Society